The Laakso-Taagepera Index in A Mean and Variance Framework

Abstract

The Laakso-Taagepera index (Laakso and Taagepera, 1979) has become the most commonly used measure to specify the ‘effective’number of political parties in a party system where parties vary substantially in their vote and/or seat shares. It is well known that the Laakso-Taagepera index is the inverse of the even more widely used Herfindahl-Hirschman index of concentration (Hirschman, 1945; Herfindahl, 1950; cf. Taagepera and Grofman, 1981). Drawing on little known work by Feld and Grofman (1977, 1980) on the so called ‘class-size paradox’, it can also be shown that both indices may be re-expressed as simple functions of a distribution's mean and variance. As far as we can judge, these latter relationships appear to be unknown in the party and electoral systems literatures. By expressing the Herfindahl-Hirschman index and the Laakso-Taagepera index in terms of means and variances we can see that each index has a ‘natural’ interpretation in terms of well known statistical parameters which allows their fundamental mathematical properties to be more clearly revealed.